Thermodynamic modeling of the condensable fraction of a gaseous effluent from lignocellulosic biomass torrefaction

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To cite this version :

Detcheberry, Mylène and Destrac, Philippe and

Massebeuf, Silvère and Baudouin, Olivier and Gerbaud, Vincent

and Condoret, Jean-Stéphane and Meyer, Xuân-Mi Thermodynamic

modeling of the condensable fraction of a gaseous effluent from

lignocellulosic biomass torrefaction. (2016) Fluid Phase Equilibria,

vol. 409. pp. 242-255. ISSN 0378-3812

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Thermodynamic modeling of the condensable fraction of a gaseous

effluent from lignocellulosic biomass torrefaction

M. Detcheberry

, P. Destrac

, S. Massebeuf

, O. Baudouin

, V. Gerbaud

,

J.-S. Condoret

, X.-M. Meyer

a_{Universit!e de Toulouse, INPT, UPS, Laboratoire de G!enie Chimique, 4, All!ee Emile Monso, F-31030 Toulouse, France} b_{CNRS, Laboratoire de G!enie Chimique, F-31030 Toulouse, France}

c_{ProSim SA, Immeuble Strat"ege A, 51 rue Amp"ere, F-31670 Lab"ege, France}

Keywords:

Reactive phase equilibria Modeling

Torrefaction Volatile matter UNIQUAC

a b s t r a c t

The condensable fraction of the gaseous effluent from the torrefaction process of wood is a complex mixture of more than one hundred oxygenated species (alcohols, acids, aldehydes, ketones, furans, phenolic, gaïacols and sugars) diluted in water where some of them are likely to react. This effluent is currently burnt to provide energy but it could be valorized as bio-sourced chemicals. To recover target products like acetic acid, glycolaldehyde, furfural and eugenol a first step of thermodynamic modeling of this complex mixture is required to be able to propose different strategies of separation-purification. This was done here by coupling the UNIQUAC model with chemical equilibria involved in the reactive mixture. Binary interaction parameters were identified using vaporeliquid equilibria data from the literature. The predicted results are in good agreement with the experimental data of systems containing water, methanol, formaldehyde, acetic acid, formic acid, propionic acid, furfural and furfuryl alcohol, main components of the considered mixture and their associated reaction products.

1. Introduction

Sustainable resources and processes are nowadays increasingly studied to propose alternatives to the use of fossil raw materials. Lignocellulosic biomass, as wood for example, is a renewable resource but its moisture content is high and it is not an easily grindable material [1]. Furthermore, its energy density is lower than coal. These issues could be overcome thanks to the torre-faction process.

Torrefaction is a thermal process carried out at temperatures below 300 !_{C, under inert atmosphere, at atmospheric pressure,}

and with residence times for the solid biomass ranging from few minutes to several hours[2,3]. Torrefied wood is a solid product constituted by more than 70% of the initial mass with properties close to those of coal. The 30% remaining part is a gaseous effluent

[2,3], composed of about one third of non condensable gases -carbon monoxide and -carbon dioxide - and two thirds of con-densable species.

Currently, torrefied wood is the main product of interest and is usually transformed into energetic gases by the gasification process

[4e6] or directly used as coal for combustion [7,8]. Conversely, gaseous by-products are considered at present time as a waste[9]

and in the best case are burned to provide energy to the process

[6]. Yet, the recovery and valorization of the condensable fraction as bio-sourced chemicals is worth considering.

An experimental study of the torrefaction of four various biomass types showed that there were significant differences in gaseous product composition depending on the nature of the biomass[10]. Condensable species composition exhibit more than one hundred oxygenated components (partially identified and quantified) and significantly differs depending on the biomass type. Any preliminary study to assess new routes, as for instance non energetic valorization of such gaseous effluent, requires knowledge of thermodynamics of these complex mixtures. Indeed, some thermodynamic models already exist for part of this mixture. In the general biorefinery field, some experimental and modeling studies of vaporeliquid equilibria have been published[11,12]. More spe-cifically, thermodynamics of formaldehyde (one of the major components of this gaseous effluent), and its mixtures with water, were developed using an approach coupling physical and chemical

* Corresponding author. Universit!e de Toulouse, INPT, UPS, Laboratoire de G!enie Chimique, 4, All!ee Emile Monso, F-31030 Toulouse, France.

E-mail address:xuan.meyer@ensiacet.fr(X.-M. Meyer).

equilibria[13,14].

This work is indeed an extension of our previously published model[13] with the aim at representing now the vaporeliquid thermodynamic behavior of the whole torrefaction condensable fraction using a combined physical and chemical model. In this paper, a strategy for modeling the vaporeliquid equilibria for a mixture of 22 representative components is proposed, including possible chemical reactions.

The paper is organized as follows. In Section1the characteristics of condensates from lignocellulosic biomass torrefaction are briefly introduced. In Section2, the strategy to develop the thermody-namic model is exposed and the choice of UNIQUAC to calculate activity coefficients is justified. Section3presents the method to estimate the unknown UNIQUAC binary interaction parameters. In Section4 the results are reported and discussed. Indeed, such a thermodynamic modeling is the pre-requisite to propose and assess (on energetic and economic criteria) different separation schemes to produce bio-sourced chemicals from the gaseous effluent of the torrefaction process. These future studies (not in the scope of this work), based on this modeling, will be able to provide the quantitative data to decide the viability of such a valorization strategy.

2. Characterization of condensates from lignocellulosic biomass torrefaction

Few descriptions of the volatile matter after torrefaction are available in the literature.Table 1gives a short inventory of the species identified in torrefaction effluents. Non condensable gases are mainly carbon monoxide and carbon dioxide. A focus on the condensable part of the volatile matter shows that condensates are a multicomponent mixture, chemically and thermally unstable, containing oxygenated species diluted in water. The oxygenated species belong to different chemical classes: water, alcohols, acids, aldehydes, ketones, furans, phenolics, gaïacols.

The main component is water accounting for 60%mol to 80%mol. Minor components are diluted in water which makes their sepa-ration a hard task. Moreover, minor components are present in proportions varying with the processed biomass[2].

As it is impossible to consider all the components present in condensates for modeling, a representative mixture was estab-lished for condensates. The analysis of the experimental data collected in the frame of INVERTO project enabled us to select an acceptable number of 22 components including: water (W), methanol (ME), formaldehyde (FA), methylene glycol (MG), hemi-formal (HF), 6 poly(oxymethylene) glycols from a degree 2 to a degree 7 (MG2eMG7), 6 poly(oxymethylene) hemiformals from a

degree 2 to a degree 7 (HF2eHF7), acetic acid (A1), formic acid (A2),

propionic acid (A3), furfural (Fu) and furfuryl alcohol (FuAl). All

these compounds are present in significant amounts (a few g/L in the condensed aqueous phase).

A previous study was dedicated to the modeling of aqueous solutions of formaldehyde and methanol [13] and the same approach is used here to be extended to the modeling of the representative mixture of the torrefaction condensates.

3. Thermodynamic model

The complexity of the condensate mixture makes its purification a difficult task and this complexity has to be handled first by a suitable thermodynamic description. An important point to emphasize is the presence of reactive components in the mixture: carboxylic acids associate in the vapor phase and formaldehyde polymerizes with water and methanol to produce hemiformal, methylene glycol, poly(oxymethylene) hemiformals and poly(oxy-methylene) glycols. So, vaporeliquid equilibria must be coupled with those chemical equilibria for a suitable description of con-densates thermodynamic behavior.

Table 1

Inventory of species identified in torrefaction effluents listed in the literature.

Chemical class CAS number Component [1] [15] [16] [17] [2] [10] Our mixture

Alcohol 67-56-1 Methanol ✓ ✓ ✓ ✓

Aldehydes and Ketones 116-09-6 Hydroxyacetone (acetol) ✓ ✓ ✓ ✓ ✓

75-07-0 Acetaldehyde ✓

141-46-8 Hydroxyacetaldehyde (glycolaldehyde) ✓ ✓ ✓

50-00-0 Formaldehyde ✓ ✓ ✓ ✓

Acids 64-19-7 Acetic acid ✓ ✓ ✓ ✓ ✓ ✓

64-18-6 Formic acid ✓ ✓ ✓ ✓ ✓ ✓

79-09-4 Propionic acid ✓ ✓ ✓

50-21-5 Lactic acid ✓ ✓

Furans 98-01-1 Furfural ✓ ✓ ✓ ✓ ✓

98-00-0 2-furanmethanol ✓ ✓

Phenolics and Gaïacols 108-95-2 Phenol ✓ ✓

90-05-1 2-methoxyphenol (gaïacol) ✓ 106-44-5 4-methylphenol (p-cresol) ✓ 93-51-6 2-methoxy-4-methylphenol (4-methylgaïcol) ✓ 2785-89-9 4-ethyl-2-methoxyphenol (4-ethylgaïacol) ✓ 91-10-1 2.6-dimethoxyphenol (syringol) ✓ 97-53-0 2-methoxy-4-prop-2-enylphenol (eugenol) ✓ 121-33-5 4-hydroxy-3-methoxybenzaldehyde (vanillin) ✓ 2-methoxy-4-(1E)-prop-1-en-1-ylphenol ✓

121-34-6 4-hydroxy-3-methoxybenzoic acid (vanillic acid) ✓

6443-69-2 1.2.3-trimethoxy-5-methylbenzene ✓

2.6-dimethoxy-4-prop-2-enylphenol ✓

1.4-hydroxy-3.5-dimethoxyphenylethanone ✓

2478-38-8 7.9-dihydroxy-3-methoxy-1-methyl-6H-dibenzo(b.d)pyran-6-one ✓

Water 7732-18-5 Water ✓ ✓ ✓ ✓ ✓ ✓

Incondensables 124-38-9 Carbon dioxide ✓ ✓ ✓ ✓ ✓

3.1. Description of the thermodynamic behavior of the reactive mixture

As mentioned above, when modeling thermodynamics of such systems, the main difficulty is to account for the coupling of chemical and physical equilibria of these reactive molecules. A re-view of thermodynamics for reactive mixtures has been given by Maurer[14]where it is suggested to uncouple the physical and the chemical phenomena in the model so as to differenciate the effects of weak intermolecular interactions of the physical equilibria from the strong intermolecular interactions involved in the chemical reactions. This modeling approach has also the advantage of avoiding spreading the uncertainty on the chemical equilibrium constant into the physical equilibrium parameters.

Fig. 1 illustrates the outline of this model. Note that in our approach the system is considered at chemical and physical equi-librium and therefore no chemical or physical kinetic data are considered.

Thus, the reactive vaporeliquid equilibrium model includes: - physical phase equilibria described using a

g

account for this multicomponent system with a large range of molar masses and volatilities. The physical interactions between all species are taken into account through activity coefficients calculation in the liquid phase and through an equation of state for the gas phase.

- 2 chemical reaction equilibria for the formation of methylene glycol and hemiformal:

- formation of methylene glycol: FA þ W#MG - formation of hemiformal: FA þ ME#HF

- 12 chemical reaction equilibria between the poly(oxy-methylene) glycols, poly(oxypoly(oxy-methylene) hemiformals:

- formation of poly(oxymethylene) glycols: MGn#1þ MG#MGnþ W

- formation of poly(oxymethylene) hemiformals: HFn#1þ HF#HFnþ ME

- 3 direct dimerization and 3 crossed dimerization chemical equilibria of acetic acid, formic acid and propionic acid are assumed to occur in the vapor phase:

- direct dimerization of a carboxylic acid Ai: 2Ai#Ai2

- crossed dimerization of Aiand Aj: Aiþ Aj#A_iA_j

where Aiand Ajcorrespond to one of the following carboxylic acid:

acetic acid, formic acid, propionic acid. A total of 20 reactions are accounted for in the description of the behavior of the reactive mixture.

Note that once the vaporeliquid equilibrium equations and the chemical reaction equilibrium equations in one phase are satisfied, the chemical-reaction equilibrium equations in the other phase are automatically satisfied.

3.2. Vapor-liquid equilibrium model

As the model will not be used under pressure, the gas phase was considered as a perfect gas where gas phase associations of car-boxylic acids; and methylene glycol and hemiformal formations are included.

To calculate the activity coefficients of the liquid phase, three models based on the local composition were considered: UNIversal Functional Activity Coefficient Original (UNIFAC Original). Non Random Two Liquids (NRTL) and UNIversal QUAsi Chemical (UNI-QUAC).Table 2synthetises a comparison of these thermodynamic models. The advantage of the UNIFAC Original model lies in its predictive capability and is interesting when experimental data are lacking. Meanwhile, its range of temperature applicability is rela-tively poor [18]. Pressure and temperature ranges of UNIQUAC applicability are greater than UNIFAC Original. Semi-empirical models like NRTL or UNIQUAC are more accurate for the binaries

for which experimental data are available. Compared to NRTL, UNIQUAC takes into account the molecule shape and size difference effects and is then more suitable for the studied asymetric mixture containing both small molecules (methanol, formaldehyde, formic acid…) and larger ones (furfural, poly(oxymethylene) glycols…).

Therefore, the UNIQUAC model was selected to describe the non-ideality of the liquid phase. UNIQUAC equations[19]are given by: ln gi¼ ln gCi þ ln gRi (1) ln gC_i ¼ ln fi x_iþ Z 2ln q_i f_iþ li# f_i x_i XnC j¼1 xjlj (2) ln gR_i ¼ qi 0 B B B @ 1 # lnXnC j¼1 q_jt_ji#X nC j¼1 q_it_ij PnC k¼1qktkj 1 C C C A (3) f_i¼PnxCiri i¼1xiri and qi¼ x_iq_i PnC i¼1xiqi (4) li¼ Z 2ðri# qiÞ # ðri# 1Þ (5) t_ij¼ exp ) #Aij RT * and t_ji¼ exp ) #Aji RT * (6)

A_ij¼ A0_ijþ AT_ij+T # T_ref, and A_ji¼ A0_jiþ AT_ji+T # T_ref, (7)

The UNIQUAC binary interaction parameters (see equation(7)) were identified for the different binaries of the condensate repre-sentative system using either experimental vaporeliquid data from literature when available or numerical data generated by UNIFAC Original[20,21]. The determination of UNIQUAC binary interaction parameters is detailed in the following part.

4. Determination of UNIQUAC binary interaction parameters UNIQUAC binary interaction parameters must be estimated for systems including water, methanol, formaldehyde, methylene gly-col, hemiformal, poly(oxymethylene) glycols (MG # MG7),

poly(-oxymethylene) hemiformals (HF # HF7), acetic acid, formic acid,

propionic acid, furfural, furfuryl alcohol. The binary interaction parameters of the formaldehyde e water e methanol reactive system were formerly identified[13]. Some binaries (like water -methanol, water - acetic acid…) have been widely studied in the

literature. Nevertheless, as the reported binary interaction param-eters may have been estimated with other values of the pure component properties than those used in this study, they were identified again in this work using experimental data recom-mended by the DECHEMA.

Different cases were considered for the binary interaction pa-rameters estimation (seeTable 3):

1. case 1: non-reactive binary systems

2. case 2: binary systems involving formaldehyde species and other components except carboxylic acids

3. case 3: binary systems involving carboxylic acids

Component abbreviations are defined in the nomenclature. The reactive vaporeliquid equilibrium of the water-methanol-formaldehyde system was already modeled[13]so the reference of the publication is given for theses binaries.

For case 1 and case 2, the same physical phase equilibrium equations were used, given by:

y_iP ¼ x_ig_iðT; xÞPS_iðTÞ (8)

The coefficients aiof the equations to calculate the vapor

pres-sure of pure component i with respect to temperature were taken from the DIPPR Database[22]available through the Simulis

Ther-modynamics package (ProSim):

ln PS

iðTÞ ¼ a1;Sþa2;ST þ a3;Sln T þ a4;STa5;S.

When available in the literature experimental vaporeliquid data were used for the identification of the UNIQUAC binary interaction parameters. When no data were available, vaporeliquid numerical data at constant vapor ratio and temperature (or pressure) were generated using the UNIFAC Original model[21,20]. As mentioned above, it was chosen to uncouple the physical and chemical phe-nomena for systems involving formaldehyde species to avoid to spread the uncertainty of the chemical equilibrium constants into the parameters of the physical equilibrium. Because of the presence of the chemical reactions, no uncoupled vaporeliquid experimental data were available in the literature. So, vaporeliquid data were generated using the UNIFAC Original model for case 2. Note that binary interaction parameters of systems labeled 2 inTable 3have to be ascertained as soon as experimental data become available.

Finally, for case 3 (binaries involving carboxylic acids), conven-tional physical phase equilibrium equations, with an association term to account for chemical equilibria, were used for the identi-fication. Nevertheless, when dealing with the dimerization equi-libria of carboxylic acids, it was found more convenient not to uncouple physical and chemical equilibria. Indeed, for these spe-cific compounds, the uncoupled approach has been developed for long[23]and was already implemented in the Prosim Plus soft-ware. In this case, it is proposed to use a correction term in equation

Table 2

Comparison of thermodynamics models based on the local composition concept.

Thermodynamic model Advantages Drawbacks

UNIFAC Original No experimental data required (predictive model) Not recommended for process design

Multicomponent vaporeliquid equilibria Not able to differenciate isomers

Poor range of temperature applicability

NRTL Multicomponent vaporeliquid and liquideliquid equilibria Large number of binary interaction parameters to identify

Widely used for flowsheeting and process design Molecule shape and size difference effects not taken into account

Experimental data taken into account in the model

UNIQUAC Multicomponent vaporeliquid and liquideliquid equilibria Large number of binary interaction parameters to identify

Widely used for flowsheeting and process design Experimental data taken into account in the model

Molecule shape and size difference effects taken into account directly in the model

(8), fV ;S_i , which accounts for the presence of the dimerization equilibria: yi fV_iðT; P; yÞ fV;S_i +T; PS iðTÞ , P ¼ xigiðT; xÞP S iðTÞ (9)

At equilibrium, components present in the vapor phase follow the perfect gas law so fV

iðT; P; yÞ ¼ 1. The correction terms, also

termed vapor fugacity coefficients of pure constituant i at satura-tion pressure, are calculated as follows:fV;S_i ¼#1þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1þ4KðTÞPS iðTÞ p 2KðTÞPS iðTÞ . Note that fV ;S_i ðT; PS

iðTÞÞ ¼ 1 for all other components.

Chemical reaction equilibrium constants are obtained as follows:

' Direct dimerization of carboxylic acid A: log KA2¼ aAþbTA

' Direct dimerization of carboxylic acid B:log KB2¼ aBþbTB

' Crossed dimerization of carboxylic acid A and carboxylic acid B: KAB¼

ffiffiffiffiffiffiffiffiffiffiffi KAKB

p

and log KAB¼ aABþbTAB

For direct dimerization, parameters aA; aB; bA; bB are taken

from the DECHEMA literature[24]:

When available, experimental data were used for the identifi-cation and simulated data were generated using UNIFAC Original when not available.

Table 4 summarizes the different cases considered for the identification of the UNIQUAC binary interaction parameters.

In the case of systems with formaldehyde species (with or without carboxylic acids), some preliminary calculations showed that it was not useful to differentiate between the binary interac-tion parameters of the poly(oxymethylene) glycols (MGn) and

poly(oxymethylene) hemiformals (HFn) from degree 2 to 7 with

other components. This indeed assumes that the interaction in the second term of the residual part of the activity coefficient for these

Table 3

Matrix of the modeling assumptions for each binary of the mixture.

A1 A2 A3 W ME FA MG MG2# MG7 HF HF2# HF7 Fu FuAl A1 e e e e e e e e e e e e A2 3 e e e e e e e e e e e A3 3 3 e e e e e e e e e e W 3 3 3 e e e e e e e e e ME 3 3 3 1 e e e e e e e e FA 3 3 3 [13] [13] e e e e e e e MG 3 3 3 [13] [13] [13] e e e e e e MG2# MG7 3 3 3 [13] [13] [13] [13] e e e e e HF 3 3 3 [13] [13] [13] [13] [13] e e e e HF2# HF7 3 3 3 [13] [13] [13] [13] [13] [13] e e e Fu 3 3 3 1 1 2 2 2 2 2 e e FuAl 3 3 3 1 1 2 2 2 2 2 1 e

1 non-reactive binary systems.

2 binary systems involving formaldehyde species and other components except carboxylic acids. 3 binary systems involving carboxylic acids.

[13]formaldehyde e methanol e water reactive system formerly identified.

Component a! ^a

Acetic acid #10.421 3166

Formic acid #10.743 3083

Propionic acid #10.843 3316

Table 4

Assumptions for the identification of UNIQUAC binary interaction parameters.

Case n# Binaries ~a calculation fcalculation Chemical equilibrium constants

1: Non-reactive binaries Methanol e water, furfural e furfuryl

alcohol, furfural e water, furfural e methanol, furfuryl alcohol e water, furfuryl alcohol e methanol

UNIQUAC Mixture of perfect gases e

2: Binaries involving formaldehyde species and components which are not carboxylic acids

Furfural e {formaldehyde, MG, HF,

MGn; HFn}, furfuryl alcohol e

{formaldehyde, MG, HF, MGn; HFn}

UNIQUAC Mixture of perfect gases Not taken into account in the

identification 3: Binaries involving carboxylic acids Acetic acid e formic acid, acetic acid e

propionic acid, acetic acid e furfural, acetic acid e furfuryl alcohol, acetic acid e methanol, acetic acid e water, acetic acid e {formaldehyde, MG, HF,

MGn; HFn}, formic acid e propionic acid,

formic acid e furfural, formic acid e furfuryl alcohol, formic acid e methanol, formic acid e water, propionic acid e furfural, formic acid e {formaldehyde, MG, HF, MGn; HFn},

propionic acid - furfuryl alcohol, propionic acid e methanol, propionic acid e water, propionic acid e {formaldehyde, MG, HF, MGn; HFn}

UNIQUAC Mixture of perfect gases þ

Association term

Not necessary because chemical equilibrium constants are already taken into account in the association term

compounds is equal to that of the poly(oxymethylene) hemiformal and poly(oxymethylene) glycol of degree 2 for all the poly(oxy-methylene) hemiformals (HFn) and poly(oxymethylene) glycol

(MGn). Finally, with this simplification, 46 sets of parameters have

to be identified.

The UNIQUAC binary interaction parameters were identified by minimizing the relative errors (see equations(10)e(19)) between experimental data when available, or simulated data generated using UNIFAC Original when not available, and UNIQUAC vapor-eliquid equilibrium calculations:

min t0 ij;tTij;t0ji;tTji Fobj (10) Fobj¼ Fobj;bubbleþ Fobj;dew nbubbleþ ndew (11)

where for (T,x,y) diagrams:

F_obj;bubble¼ X nbubble l¼1 +/ / /y bubble

1;exp # ybubble1;calc

/ / / , l + ybubble₁ , l þ +/ / /y bubble

2;exp # ybubble2;calc

/ / / , l + ybubble₂ , l þ +/ / /P bubble

exp # Pcalcbubble

/ / / , l + Pbubble, l (12) Table 5

Binary interaction parameters estimated from literature data.

Component 1 Component 2 A0

ij A0ji ATij ATji References of data used for the identification

Acetic acid Formic acid #174 #173 #0.36 1.50 [25e27]

Acetic acid Furfural 379 #482 #0.02 0.79 [28]

Acetic acid Methanol 130 1189 0.91 #4.52 [29,30]

Acetic acid Propionic acid #46 52 #0.05 0.16 [31e33,25,26]

Acetic acid Water 46 306 #1.00 0.60 [35,36,34]

Formic acid Furfural 1904 #316 #6.00 3.90 [37]

Formic acid Propionic acid #828 1539 1.83 #3.00 [25,26,32]

Formic acid Water #205 #205 #0.17 0.20 [36]

Furfural Furfuryl alcohol 533 #570 0.05 0.67 [38]

Furfural Methanol 751 1106 #0.93 #3.36 [39]

Furfural Water 475 691 #1.70 0.12 [25,41]

Furfuryl alcohol Water 118 82 #1.37 2.05 [42,43]

Propionic acid Methanol 1156 #101 #0.38 #1.33 [44]

Propionic acid Water 157 211 #1.09 1.50 [36]

Methanol Water 156 #369 0.91 0.20 [45,46]

Table 6

Binary interaction parameters estimated from UNIFAC.

Component 1 Component 2 A0

ij A0ji ATij ATji

Formaldehyde Acetic acid 396 #613 #0.95 1.10

Formaldehyde Formic acid 290 #499 0.89 0.10

Formaldehyde Furfural 102 #107 #0.60 0.20

Formaldehyde Furfuryl alcohol 51 89 #0.14 #0.79

Formaldehyde Propionic acid 372 #572 #1.00 1.10

Methylene Glycol (MG) Acetic acid #29 375 #1.29 2.00

Methylene glycol (MG) Formic acid #78 74 0.14 #0.90

Methylene glycol (MG) Furfural #218 836 #1.44 1.50

Methylene glycol (MG) Furfuryl alcohol #545 359 #0.24 #0.47

Methylene glycol (MG) Propionic acid #100 615 #0.74 2.00

Poly(oxymethylene) glycols ðMGi; i(2Þ Acetic acid #733 936 #0.01 #1.50

Poly(oxymethylene) glycols ðMGi; i(2Þ Formic acid #474 #46 #0.38 #0.12

Poly(oxymethylene) glycols ðMGi; i(2Þ Furfural 470 #126 0.62 #1.50

Poly(oxymethylene) glycols ðMGi; i(2Þ Furfuryl alcohol 664 #195 0.34 #1.49

Poly(oxymethylene) glycols ðMGi; i(2Þ Propionic acid 30 #136 0.47 #0.83

Hemiformal (HF) Acetic acid 16 #22 0.54 #1.03

Hemiformal (HF) Formic acid 14 #29 #0.07 #0.73

Hemiformal (HF) Furfural 91 #75 0.66 #1.50

Hemiformal (HF) Furfuryl alcohol 103 #85 0.97 #1.50

Hemiformal (HF) Propionic acid 470 #309 #0.24 #0.24

Poly(oxymethylene) hemiformals ðHFi;i(2Þ Acetic acid #355 32 #0.20 #0.27

Poly(oxymethylene) hemiformals ðHFi; i(2Þ Formic acid #468 #13 #0.21 #0.22

Poly(oxymethylene) hemiformals ðHFi; i(2Þ Furfural 290 #116 0.37 #1.48

Poly(oxymethylene) hemiformals ðHFi; i(2Þ Furfuryl alcohol 1207 #454 #1.11 #0.87

Poly(oxymethylene) hemiformals ðHFi; i(2Þ Propionic acid #54 51 #0.15 #0.59

Acetic acid Furfuryl alcohol 435 #374 0.13 #0.12

Formic acid Furfuryl alcohol 107 #175 1.00 #0.30

Formic acid Methanol #402 675 0.00 0.00

Furfural Propionic acid #414 883 #0.04 #0.34

Furfuryl alcohol Methanol 440 #388 #0.46 0.54

F_obj;dew¼X ndew l¼1 +/ / /x dew

1;exp# xdew1;calc

/ / / , l + xdew₁ , l þ +/ / /x dew

2;exp# xdew2;calc

/ / / , l + xdew₂ , l þ +/ / /P dew exp # Pcalcdew

/ / / , l + Pdew, l (13)

and for (P,x,y) diagrams:

Fobj;bubble¼ X nbubble l¼1 +/ / /y bubble

1;exp # ybubble1;calc

/ / / , l + ybubble₁ , l þ +/ / /y bubble

2;exp # ybubble2;calc

/ / / , l + ybubble₂ , l þ +/ / /T bubble

exp # Tcalcbubble

/ / / , l + Tbubble, l (14) F_obj;dew¼X ndew l¼1 +/ / /x dew

1;exp# xdew1;calc

/ / / , l + xdew₁ , l þ +/ / /x dew

2;exp# xdew2;calc

/ / / , l + xdew₂ , l þ +/ / /T dew exp # Tcalcdew

/ / / , l + Tdew, l (15) with + yindex_k , l¼ yindex k;expþ yindexk;calc

2 with k2½1; 2* and index

¼ bubble or dew (16)

+

xindex_k ,

l¼

xindex k;expþ xindexk;calc

2 with k2½1; 2* and index

¼ bubble or dew (17)

+

Pindex,

l¼

Pindex_exp þ P_calcindex

2 with index ¼ bubble or dew (18)

+

Tindex,

l¼

Tindex exp þ Tcalcindex

2 with index ¼ bubble or dew (19)

The identification was performed using the Excel solver which

Table 7

Average deviation of the gas-phase composition and average deviation of the pressure or temperature for binary vaporeliquid and chemical equilibria plotted inFigs. 2 and 3.

Compound 1 Compound 2 Type of diagram DT or DPð%Þ Dy1ð%Þ References

Formic acid Acetic acid T ¼ 70!_{C 2.38 2.08 [25]}

Formic acid Acetic acid T ¼ 30!_{C 4.37 3.52 [26]}

Formic acid Acetic acid P ¼ 1013 mbar 0.21 3.05 [27]

Acetic acid Furfural P ¼ 493 mbar 0.77 1.22 [28]

Acetic acid Furfural P ¼ 890 mbar 0.39 0.95 [28]

Acetic acid Methanol P ¼ 1013 mbar 3.24 4.86 [30]

Acetic acid Methanol P ¼ 941 mbar 1.00 4.23 [29]

Acetic acid Propionic acid T ¼ 70!_{C 2.03 0.51 [25]}

Acetic acid Propionic acid T ¼ 40!_{C 1.00 0.87 [33]}

Acetic acid Propionic acid T ¼ 30!_{C 8.07 10.39 [26]}

Acetic acid Propionic acid P ¼ 1000 mbar 0.04 2.59 [32]

Acetic acid Propionic acid P ¼ 1013 mbar 3.51 1.69 [31]

Water Acetic acid P ¼ 1013 mbar 0.22 1.07 [34]

Water Acetic acid P ¼ 167 mbar 0.61 0.50 [35]

Water Acetic acid P ¼ 333 mbar 0.11 0.41 [35]

Water Acetic acid P ¼ 93 mbar 0.78 8.88 [36]

Formic acid Furfural P ¼ 1013 mbar 0.57 8.10 [37]

Formic acid Propionic acid T ¼ 70!_{C 2.09 1.68 [25]}

Formic acid Propionic acid T ¼ 30!_{C 2.76 6.98 [26]}

Formic acid Propionic acid P ¼ 1000 mbar 0.34 3.92 [32]

Formic acid Propionic acid P ¼ 1013 mbar 0.33 e [31]

Water Formic acid P ¼ 1013 mbar 0.12 1.01 [36]

Water Formic acid P ¼ 266 mbar 0.25 3.48 [36]

Water Formic acid P ¼ 93 mbar 0.66 3.67 [36]

Furfural Furfuryl alcohol P ¼ 33 mbar 0.54 8.73 [38]

Methanol Furfural P ¼ 400 mbar e 11.76 [39]

Water Furfural P ¼ 1013 mbar 1.00 2.34 [40]

Water Furfural P ¼ 946 mbar 1.12 1.02 [41]

Water Furfuryl alcohol P ¼ 40 mbar 7.39 0.75 [43]

Water Furfuryl alcohol P ¼ 73 mbar 3.08 0.82 [42]

Propionic acid Methanol T ¼ 25!_{C 1.53}

e [44]

Propionic acid Methanol T ¼ 27!_{C 1.67}

e [44]

Propionic acid Methanol T ¼ 35!_{C 1.63}

e [44]

Propionic acid Methanol T ¼ 45!_{C 1.20}

e [44]

Propionic acid Water P ¼ 1013 mbar 0.83 1.98 [36]

Propionic acid Water P ¼ 266 mbar 0.68 1.41 [36]

Propionic acid Water P ¼ 93 mbar 0.73 1.29 [36]

Water Methanol P ¼ 1013 mbar 0.18 1.90 [45]

Water Methanol P ¼ 666 mbar 0.43 3.58 [46]

Water Methanol P ¼ 466 mbar 0.84 5.46 [46]

provides a multidimensional constrained non-linear method of minimization (non-linear GRG method), coupled with the Simulis Thermodynamics add-in for estimation of thermodynamic properties.

5. Results and discussions

5.1. UNIQUAC binary interaction parameters estimation

The UNIQUAC binary interaction parameters estimated in this work are reported inTables 4and5. For all data points used in this work, the mean relative error was calculated as Fobj¼ 5:60% with

nexp¼ 671. This relatively low value indicates a good estimation of

the UNIQUAC binary interaction parameters as can be seen from the graphical comparisons of experimental data and calculated data presented in the Section 4.2.

Table 5 reports the values of the estimated UNIQUAC binary interaction parameters for which literature vaporeliquid data were available.Table 6reports the binary interaction parameters of bi-naries for which no experimental data were available in literature. Excluding systems with formaldehyde species, few binaries are concerned. Nonetheless, interactions between formaldehyde spe-cies and other components like carboxylic acids were not studied in the literature. 0 0.2 0.4 0.6 0.8 1 30 40 50 60 70 80 90 100 110 x 1, y1 T eq (°C)

[a] Water (1) ! Formic Acid (2) P = 1013 mbar P = 266 mbar P = 93 mbar 0 0.2 0.4 0.6 0.8 1 40 50 60 70 80 90 100 110 120 x 1, y1 T eq (°C)

[b] Water (1) ! Acetic Acid (2)

P = 1013 mbar P = 167 mbar P = 333 mbar P = 93 mbar 0 0.2 0.4 0.6 0.8 1 40 60 80 100 120 140 160 x 1, y1 T eq (°C)

[c] Water(1) ! Propionic Acid (2) P = 1013 mbar P = 266 mbar P = 93 mbar 0 0.2 0.4 0.6 0.8 1 90 100 110 120 130 140 150 160 170 x 1, y1 T eq (°C) [d] Water (1) ! Furfural(2) P = 1013 mbar

Fig. 2. Prediction of azeotropic systems vaporeliquid and chemical equilibria at different pressures and temperatures. (+) experimental data from the literature. Solid line: pre-dicted phase diagram with UNIQUAC model coupled to chemical equilibria.

5.2. Comparison of the UNIQUAC model with binary vaporeliquid data used for the identification

This section presents the comparison of each set of experi-mental data used for the identification with the calculated data obtained with the estimated UNIQUAC binary interaction parame-ters. References of the experimental data are indicated inTable 7.

For each binary system, the average deviation of the vapor composition and the average deviation of the pressure - in the case of (T,x,y) diagrams or the average deviation for the temperature -in the case of (P,x,y) diagrams - between experimental data and our work were calculated as:

Dy₁¼ 1 nexp X nexp l¼1 +/ / /y1;exp# y1;calc / / / , l y_1;l (20) DP ¼ 1 nexp X nexp l¼1 0/ /P_exp# P_calc / / 1 l P_l (21) DT ¼ 1 nexp X nexp l¼1 0/ /Texp# Tcalc / / 1 l Tl (22) 0 0.2 0.4 0.6 0.8 1 60 70 80 90 100 110 120 x 1, y1 T eq (°C)

[a] Methanol (1) ! Acetic Acid (2) P = 941 mbar P = 1013 mbar 0 0.2 0.4 0.6 0.8 1 20 30 40 50 60 70 80 90 100 110 x 1, y1 T eq (°C)

[b] Water (1) ! Furfuryl Alcohol (2) P = 40 mbar P = 73 mbar 0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x 1 y 1 [c] Methanol (1) ! Furfural (2) P = 1013 mbar 0 0.2 0.4 0.6 0.8 1 66 68 70 72 74 76 78 80 82 84 86 x 1, y1 T eq (°C)

[d] Furfural (1) ! Furfuryl Alcohol (2) P = 33 mbar

Fig. 3. Prediction of binary systems vaporeliquid and chemical equilibria at different pressures and temperatures. (+) experimental data from the literature. Solid line: predicted phase diagram with UNIQUAC model coupled to chemical equilibria.

with: y_1;l¼ + y1;expþ y1;calc , l 2 (23) P_l¼0Pexpþ Pcalc 1 l 2 (24) Tl¼ 0Texpþ Tcalc 1 l 2 (25)

Table 7 presents the average deviation for the gas-phase composition and the average deviation for the equilibrium pressure (or temperature) between experimental data from the literature and the model, for all binary systems plotted inFigs. 2 and 3. Pressure and temperature deviations are between 0.04% and 8.07%, and gas-phase composition deviations between 0.41% and 11.76%. These values indicate that the UNIQUAC model developed in this work provides a fairly good description of the different binary systems, for large pressure and composition ranges. Note that all deviation values are very similar, which means that the quality of the prediction is similar for all binary

systems.

Fig. 2shows the isobaric diagram of the following binary systems: (a) water formic acid; (b) water acetic acid; (c) water -propionic acid; (d) water - furfural. Good agreement was obtained between experimental data and the prediction of the azeotropic point at different pressures for all systems.

Fig. 3 presents the isobaric diagram of the following binary systems: (a) methanol - acetic acid; (b) water - furfuryl alcohol; (c) methanol - furfural; (d) furfural - furfuryl alcohol. Note that some inconsistent experimental points explain the larger deviation observed between the model and the experimental data.

Globally, all the figures and table confirm that estimated binary interaction coefficients give a good representation of all binaries. Every experimental data used for the identification are indeed adequately represented by the model.

5.3. Validation of the model from comparison with ternary vaporeliquid reactive equilibria

The complete reactive vaporeliquid model was used to validate the use of the binary interaction parameters for a ternary system. The model includes equations for the vaporeliquid equilibrium

Table 8

Chemical reaction equilibrium constants: ln K ¼ a1þ a2=T.

Reaction Phase Heat of reaction (kJ/mol) a1 a2 References

W þ FA⇔MG Vapor #43.51 #16.984 5233.2 [50] 2MG⇔MG2þ W Liquid #0.234 4.98.10#3 869.5 [51,20] MG þ MG2⇔_{MG3þ W} MG þ MG3⇔_{MG4þ W} MG þ MG4⇔MG_{5þ W} Liquid _#0.234 1.908.10#2 544.5 [51,20] MG þ MG5⇔MG_{6þ W} MG þ MG6⇔MG_{7þ W} ME þ FA⇔HF Vapor #53.73 #14.755 5969.4 [49] 2HF⇔HF2þ ME HF þ HF2⇔_{HF3þ ME} HF þ HF3⇔_{HF4þ ME Liquid #7.00 #0.4966 #491.3 [49]} HF þ HF4⇔HF_{5þ ME} HF þ HF5⇔HF_{6þ ME} HF þ HF6⇔HF_{7þ ME} Table 9

Average deviation of the gas-phase composition and average deviation of the temperature for ternary vaporeliquid and chemical equilibria illustrated inTables 10e13

Compound 1 Compound 2 Compound 3 P ðmbarÞ DTð%Þ Dy1ð%Þ Dy2ð%Þ References

Water Acetic acid Propionic acid 1013 0.53 4.29 6.05 [53]

Water Formic acid Acetic acid 67 1.44 2.74 4.61 [54]

Water Formic acid Acetic acid 1013 0.22 2.63 4.51 [55]

Methanol Water Acetic acid 1013 1.03 4.19 5.19 [52]

Water Methanol Furfural 1007 e 9.38 9.14 [56]

Water Methanol Furfural 400 e 7.47 9.59 [56]

Table 10

Prediction of vaporeliquid reactive equilibria of water (1) e acetic acid (2) e propionic acid (3) ternary system[53].

P ðmbarÞ x1 x2 Teq;expð!CÞ Teq;calcð!CÞ DT ð%Þ y1;exp y1;calc Dy1ð%Þ y2;exp y2;calc Dy2ð%Þ

1013 0.20 0.16 114.0 112.7 1.18 0.505 0.557 9.72 0.141 0.125 11.94 1013 0.63 0.07 102.3 102.4 0.08 0.825 0.821 0.46 0.038 0.041 6.54 1013 0.80 0.04 100.4 101.1 0.65 0.876 0.881 0.58 0.024 0.024 1.05 1013 0.20 0.32 113.0 112.3 0.63 0.438 0.490 11.28 0.282 0.257 9.35 1013 0.20 0.48 112.2 111.7 0.44 0.391 0.431 9.70 0.420 0.392 6.92 1013 0.60 0.24 102.7 103.0 0.26 0.762 0.764 0.32 0.151 0.149 1.06 1013 0.80 0.12 100.5 101.3 0.77 0.872 0.868 0.45 0.074 0.078 5.40 1013 0.2 0.64 111.3 110.9 0.33 0.358 0.378 5.48 0.537 0.529 1.50 1013 0.40 0.48 106.4 105.9 0.50 0.567 0.594 4.71 0.353 0.339 3.91 1013 0.71 0.23 101.8 102.0 0.21 0.817 0.811 0.73 0.143 0.152 6.27 1013 0.80 0.16 101.1 101.4 0.28 0.867 0.862 0.52 0.102 0.109 6.59

(see equation (26)) and the chemical reaction equilibrium (see equations(30)e(33)).

Values of the chemical reaction equilibrium constants were taken from the literature[24,47e49].

y_iP ¼ x_ig_iðT; xÞPS_iðTÞfV;S_i +T; P_iSðTÞ, (26) ln P_iSðTÞ ¼ a1þ a2 T þ a3ln T þ a4T a5 ₍₂₇₎ 8 > > > > < > > > > : fV;S_i +T; PS_iðTÞ,¼#1 þ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ 4KðTÞPS_iðTÞ q

2KðTÞPS_iðTÞ for carboxylic acids fV;S_i +T; PS_iðTÞ,¼ 1 otherwise (28) log KðTÞ ¼ a₁þa2 T (29) KMG¼ yMG yFAyW$ Pref P (30) Table 12

Prediction of vaporeliquid reactive equilibria of water (1) e formic acid (2) e acetic acid (3) ternary system[54,55].

P ðmbarÞ x1 x2 Teq;expð!CÞ Teq;calcð!CÞ DT ð%Þ y1;exp y1;calc Dy1ð%Þ y2;exp y2;calc Dy2ð%Þ

67 0.20 0.16 42.4 42.0 0.89 0.237 0.232 1.97 0.210 0.189 10.70 67 0.40 0.12 41.3 41.1 0.60 0.446 0.464 3.85 0.119 0.110 7.44 67 0.20 0.32 40.0 40.6 1.54 0.187 0.175 6.46 0.377 0.378 0.39 67 0.40 0.24 41.0 41.1 0.24 0.405 0.413 1.85 0.244 0.239 2.08 67 0.60 0.16 40.2 40.5 0.77 0.625 0.648 3.69 0.137 0.125 9.05 67 0.80 0.08 39.0 39.6 1.49 0.838 0.848 1.22 0.047 0.046 1.25 67 0.20 0.48 37.7 38.9 3.26 0.129 0.132 2.11 0.573 0.564 1.60 67 0.40 0.36 40.2 41.0 1.94 0.354 0.364 2.75 0.404 0.382 5.65 67 0.60 0.24 40.3 41.0 1.63 0.626 0.632 0.91 0.214 0.202 5.93 67 0.20 0.64 36.2 37.1 2.54 0.100 0.099 1.36 0.755 0.747 1.06 67 0.40 0.48 40.0 40.8 1.93 0.300 0.319 6.25 0.576 0.541 6.33 67 0.60 0.32 40.8 41.5 1.64 0.615 0.617 0.40 0.300 0.289 3.80 1013 0.20 0.16 109.2 109.3 0.13 0.250 0.273 8.79 0.160 0.171 6.68 1013 0.20 0.32 107.3 108.4 1.04 0.228 0.227 0.38 0.337 0.341 1.23 1013 0.20 0.64 106.0 106.4 0.41 0.150 0.164 8.82 0.713 0.681 4.53 1013 0.40 0.12 106.3 106.2 0.08 0.500 0.516 3.17 0.101 0.099 2.36 1013 0.40 0.24 106.7 106.6 0.09 0.454 0.480 5.54 0.217 0.209 3.69 1013 0.40 0.36 106.8 106.9 0.10 0.445 0.447 0.46 0.335 0.330 1.56 1013 0.40 0.48 107.1 107.2 0.08 0.393 0.418 6.23 0.482 0.461 4.41 1013 0.60 0.08 103.8 103.7 0.09 0.690 0.709 2.65 0.058 0.051 12.16 1013 0.60 0.16 104.4 104.3 0.08 0.690 0.698 1.14 0.114 0.109 4.08 1013 0.60 0.24 105.3 104.9 0.35 0.690 0.688 0.26 0.181 0.174 4.00 1013 0.60 0.32 105.3 105.6 0.29 0.690 0.681 1.37 0.229 0.245 6.71 1013 0.80 0.04 101.9 101.8 0.06 0.860 0.862 0.23 0.023 0.021 9.88 1013 0.80 0.08 102.0 102.2 0.20 0.866 0.867 0.08 0.044 0.043 2.64 1013 0.80 0.12 102.4 102.6 0.18 0.872 0.872 0.01 0.068 0.066 3.30 1013 0.80 0.16 102.7 103.0 0.30 0.876 0.879 0.30 0.089 0.089 0.39 Table 11

Prediction of vaporeliquid reactive equilibria of methanol (1) e water (2) e acetic acid (3) ternary system[52].

P ðmbarÞ x1 x2 Teq;expð!CÞ Teq;calcð!CÞ DT ð%Þ y1;exp y1;calc Dy1ð%Þ y2;exp y2;calc Dy2ð%Þ

1013 0.1148 0.6056 93.4 93.7 0.4 0.3442 0.3316 3.74 0.5361 0.5480 2.20 1013 0.0344 0.6787 99.6 99.3 0.3 0.1312 0.1203 8.66 0.7030 0.7077 0.67 1013 0.3555 0.5899 79.0 77.8 1.5 0.7039 0.7051 0.17 0.2682 0.2889 7.43 1013 0.3362 0.5591 80.6 79.7 1.1 0.7079 0.6801 4.01 0.2790 0.3051 8.93 1013 0.3795 0.5258 79.4 78.1 1.7 0.7237 0.7153 1.17 0.2608 0.2734 4.70 1013 0.1641 0.7961 85.3 85.2 0.1 0.5407 0.5142 5.03 0.4492 0.4771 6.01 1013 0.4069 0.5223 78.6 76.7 2.4 0.7530 0.7373 2.10 0.2394 0.2555 6.49 1013 0.0264 0.3894 104.6 103.9 0.7 0.0776 0.0731 5.96 0.5010 0.5223 4.16 1013 0.1268 0.5316 94.3 94.2 0.2 0.3741 0.3424 8.84 0.4867 0.5077 4.23 1013 0.0399 0.6684 98.9 98.9 0.0 0.1515 0.1367 10.24 0.6897 0.6923 0.38 1013 0.4386 0.4855 77.4 76.0 1.7 0.7765 0.7568 2.57 0.2157 0.2359 8.96 1013 0.4177 0.4968 78.5 76.8 2.2 0.7376 0.7427 0.69 0.2506 0.2484 0.88 1013 0.0467 0.6815 98.3 98.2 0.1 0.1786 0.1608 10.50 0.6782 0.6857 1.09 1013 0.3395 0.5184 81.4 80.5 1.1 0.6892 0.6763 1.90 0.2676 0.3014 11.89 1013 0.2225 0.5762 87.8 86.5 1.5 0.5558 0.5370 3.43 0.3869 0.4102 5.85 1013 0.3985 0.5217 78.7 77.2 2.0 0.7500 0.7306 2.62 0.2411 0.2608 7.85 1013 0.0702 0.5801 97.9 97.6 0.3 0.2190 0.2115 3.50 0.5949 0.6015 1.10 1013 0.0889 0.6060 95.7 95.8 0.1 0.2865 0.2667 7.16 0.5717 0.5854 2.37 1013 0.3583 0.5865 78.6 77.7 1.1 0.7309 0.7069 3.33 0.2634 0.2870 8.57

KMGn¼ xMGnxW xMGxMGn#1 $ g_MGng_W g_MGg_MGn#1 with n2½2; 7* (31) KHF¼_yyHF FAyME$ P_ref P (32) KHFn¼ xHFnxME xHFn#1xHF $ g_HFng_ME g_HF n#1gHF with n2½2; 7* (33)

In this work, the chemical reaction constants (seeTable 8) are expressed in the gas phase for the formation of methylene glycol (eq.(29)) and hemiformal (eq.(31)).

Binary vapor liquid data were used to regress the UNIQUAC bi-nary interaction parameters and terbi-nary vapor liquid data to

validate the model and to check the extensibility of the model to multicomponent mixtures. Experimental data were taken from the DECHEMA literature in the same ranges of pressure and tempera-ture where the model has been identified.

The reactive vapor liquid equilibrium of the ternary water-methanol-formaldehyde mixture was already validated in a former publication [13]. No data were available to validate the model on other systems.

Tables 10e13give the corresponding values and relative errors of all isobaric diagrams of the following systems: methanol - water acetic acid; water formic acid acetic acid; water acetic acid -propionic acid; methanol - water - furfural.Table 9 reports the average deviation of the equilibrium temperature and the average deviation of the gas-phase composition between experimental data from the literature ([52e56]) and our model, for ternary systems of

Table 13

Prediction of vaporeliquid reactive equilibria of methanol (1) e water (2) e furfural (3) ternary system[56].

P ðmbarÞ x1 x2 y1;exp y1;calc Dy1ð%Þ y2;exp y2;calc Dy2ð%Þ

1007 0.0023 0.9956 0.0168 0.0161 4.02 0.9714 0.9686 0.28 1007 0.0183 0.9654 0.1316 0.1019 25.4 0.8052 0.8296 2.99 1007 0.0237 0.8866 0.1057 0.0959 9.73 0.8156 0.8049 1.32 1007 0.0447 0.5827 0.1611 0.1334 18.7 0.7714 0.8073 4.55 1007 0.0300 0.9600 0.1633 0.1640 0.44 0.8003 0.7921 1.03 1007 0.1139 0.2025 0.5025 0.4192 18.0 0.4666 0.4998 6.86 1007 0.0431 0.9425 0.2265 0.2136 5.86 0.7231 0.7359 1.75 1007 0.1443 0.3721 0.4679 0.3959 16.6 0.4959 0.5550 11.2 1007 0.0809 0.8111 0.3014 0.2630 13.6 0.6511 0.6688 2.69 1007 0.0614 0.9284 0.3447 0.2859 18.6 0.6246 0.6805 8.57 1007 0.1836 0.3266 0.5688 0.4830 16.3 0.4056 0.4717 15.0 1007 0.1222 0.7963 0.4299 0.3703 14.8 0.5315 0.5741 7.71 1007 0.1597 0.6628 0.4386 0.4021 8.67 0.5248 0.5541 5.43 1007 0.2077 0.4922 0.5781 0.4752 19.5 0.3949 0.4885 21.1 1007 0.2307 0.4103 0.5932 0.5230 12.5 0.3862 0.4418 13.4 1007 0.1791 0.7164 0.5179 0.4587 12.1 0.4535 0.4991 9.57 1007 0.2416 0.5369 0.5891 0.5227 11.9 0.3891 0.4447 13.3 1007 0.3711 0.1649 0.7821 0.7816 0.06 0.2043 0.1884 8.12 1007 0.2082 0.7182 0.5752 0.5176 10.5 0.4013 0.4467 10.7 1007 0.3488 0.3721 0.7009 0.6631 5.55 0.2846 0.3116 9.05 1007 0.3010 0.5313 0.6597 0.5995 9.56 0.3232 0.3733 14.4 1007 0.4954 0.1467 0.8393 0.8526 1.58 0.1440 0.1264 12.9 1007 0.3500 0.5333 0.6779 0.6559 3.30 0.3081 0.3217 4.33 1007 0.5497 0.1566 0.8445 0.8649 2.38 0.1359 0.1174 14.5 1007 0.3283 0.6097 0.7079 0.6537 7.95 0.2766 0.3259 16.3 1007 0.3364 0.6131 0.6891 0.6664 3.36 0.2996 0.3155 5.17 1007 0.3645 0.5814 0.7145 0.6870 3.92 0.2734 0.2962 7.99 1007 0.3545 0.6304 0.7323 0.7035 4.02 0.2608 0.2888 10.2 1007 0.4902 0.4628 0.7656 0.7731 0.97 0.2295 0.2168 5.71 1007 0.9023 0.0902 0.9699 0.9601 1.01 0.0295 0.0389 27.5 400 0.0011 0.9983 0.0074 0.0085 14.0 0.9897 0.9859 0.39 400 0.0677 0.1470 0.4166 0.3887 6.92 0.5057 0.5082 0.49 400 0.0687 0.6107 0.1752 0.2206 22.9 0.7661 0.7293 4.93 400 0.1422 0.2299 0.5441 0.5216 4.22 0.4098 0.4275 4.22 400 0.0413 0.9548 0.2758 0.2353 15.8 0.7106 0.7432 4.48 400 0.0703 0.8125 0.2163 0.2501 14.4 0.7184 0.6772 5.91 400 0.1867 0.4647 0.4566 0.4884 6.72 0.5072 0.4776 6.02 400 0.2806 0.2329 0.6398 0.7092 10.2 0.3303 0.2617 23.1 400 0.1150 0.8743 0.4504 0.4462 0.94 0.5237 0.5269 0.61 400 0.1966 0.6213 0.4107 0.4935 18.3 0.5551 0.4698 16.6 400 0.1209 0.8732 0.4405 0.4683 6.13 0.5472 0.5158 5.91 400 0.1586 0.7753 0.4539 0.4705 3.60 0.5076 0.4814 5.31 400 0.2681 0.4990 0.5412 0.5947 9.42 0.4256 0.3774 12.0 400 0.3312 0.3927 0.6321 0.6797 7.25 0.3374 0.2969 12.7 400 0.1910 0.7606 0.5397 0.5341 1.05 0.4473 0.4277 4.49 400 0.1960 0.7521 0.5078 0.5386 5.88 0.4686 0.4235 10.1 400 0.3354 0.4969 0.5939 0.6675 11.6 0.3798 0.3088 20.6 400 0.2393 0.7539 0.6280 0.6375 1.51 0.3659 0.3541 3.28 400 0.3137 0.6056 0.6353 0.6577 3.46 0.3414 0.3175 7.25 400 0.3715 0.5872 0.7285 0.7203 1.13 0.2464 0.2636 6.76 400 0.5327 0.3226 0.7737 0.8219 6.04 0.2095 0.1636 24.6 400 0.4749 0.5098 0.7722 0.7951 2.92 0.2204 0.1992 10.1 400 0.6550 0.3149 0.8477 0.8744 3.10 0.1453 0.1200 19.1 400 0.7800 0.1907 0.9075 0.9243 1.83 0.0880 0.0713 20.9

Tables 10e13Note that these data were not used for the estimation of the binary interaction parameters but only to validate the approach. Temperature deviations are between 0.22% and 1.44%. and gas-phase composition deviations between 2.63% and 9.59%. This good agreement confirms that our model is able to represent the behavior of multicomponent systems.

As mentioned above, good agreement was obtained between experimental data set and estimated vaporeliquid equilibria with our model.

6. Conclusion

In this work a model to describe the thermodynamic behavior of a complex reactive mixture was developed. The model was applied to a representative mixture of the condensable fraction of the gaseous effluent from the wood torrefaction process. A model based on the local composition concept (UNIQUAC) was chosen and was coupled to chemical equilibria of this reactive mixture where 22 compounds and 14 chemical reactions are considered. With this uncoupling approach, effects of weak intermolecular interactions of the physical equilibria are differentiated from the strong intermo-lecular interactions involved in the chemical reactions. In the pre-sent case, chemical equilibrium constants were available in the literature and can then be considered as known. The hypothesis of similar interactions for poly(oxymethylene) glycols with other compounds and for poly(oxymethylene) hemiformals with other compounds allowed to limit to 46 the number of unknown vaporeliquid equilibrium binary interaction parameters. They were identified here from litterature data for binary systems when available or from simulated data when not. This approach was validated by comparison with available experimental data for multicomponent systems.

This modeling was done with the purpose of designing separation-purification process for valorization of the gaseous effluent of the torrefaction process for bio-sourced chemicals. Nevertheless, we are confident that this approach, developed here for a specific application, can be generic to describe other complex thermodynamic systems including reactive components.

Acknowledgments

The authors gratefully acknowledge financial support by the French Agence Nationale de la Recherche and also the partners of the INVERTO project (ANR-12-BIME-0008-04): CEA (Grenoble, France), CIRAD (Montpellier, France) and PCAS (Longjumeau, France).

Nomenclature

Mathematical symbols

Ai;j; Aj;i UNIQUAC binary interaction parameters of the

components i and j (cal/mol) F_obj objective function

K chemical reaction equilibrium constant n degree of polymerization

nC number of components

nexp number of experimental data point

P pressure of the system PS

i equilibrium vapor pressure of pure component i

qi Van der Waals area parameter of the component i

ri Van der Waals volume parameter of the component i

T temperature of the system (K)

T_ref temperature at the reference state: T_ref ¼ 298:15K Tref Tref ¼ 298:15!C

xi liquid molar fraction of the component i

yi vapor molar fraction of the component i

Z lattice coordination number set equal to 10 Components

Ai carboxylic acid

Ai2 carboxylic acid dimer

FA Formaldehyde Fu Furfural FuAl Furfuryl Alcohol HF hemiformal HFn poly(oxymethylene) hemiformal ME methanol MG methylene glycol MGn poly(oxymethylene) glycol W water Greek symbols

gi activity coefficient of the component i

fi UNIQUAC volume fraction of the component i

fV;S_i vapor fugacity coefficient of pure constituant i at saturation pressure

fV_i vapor fugacity coefficient of constituant i in the mixture ti;j; tj;i binary interaction characteristic energy parameters of the

components i and j

qi UNIQUAC area fraction of the component i

Subscripts

calc calculated exp experimental

i; j; k index of the components l index of the experimental points ref reference state

Superscripts

bubble bubble point C combinatorial term dew dew point

R residual term S saturation point References

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